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Prove that every rational function is co...

Prove that every rational function is continuous.

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To prove that every rational function is continuous, we will follow these steps: ### Step 1: Definition of a Rational Function A rational function can be expressed in the form \( f(x) = \frac{p(x)}{q(x)} \), where \( p(x) \) and \( q(x) \) are polynomial functions. ### Step 2: Continuity of Polynomial Functions Polynomial functions are continuous everywhere. This means that both \( p(x) \) and \( q(x) \) are continuous functions for all values of \( x \). ...
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